Abstract

It is noted that in large eddy simulation(LES), filtering of the three-point third-order velocity correlation allows one to determine the two-point third-order correlation of the filtered velocity. This is useful in analyzing the dynamics of filtered (LES) fields, since the two-point third-order correlation describes energy flux from large to small scales, just as it does in unfiltered turbulence. A model for the three-point third-order correlation for stationary, incompressible, homogeneous, isotropic turbulence in the inertial range is proposed in which simple polynomials are used as the scalar function appearing in the most general tensorial form for the correlation. This leads to a model with four free parameters, which are set by appealing to statistical data from a direct numerical simulation. The resulting three-point third-order correlation function is in very good agreement with the data.

Received 18 April 2007Accepted 29 August 2007Published online 26 October 2007

Acknowledgments:

The authors would like to thank Dr. Amitabh Bhattacharya, who helped with the analysis, and Dr. Paulo Zandonade, who provided the DNS data. The support of the National Science Foundation (CTS-0352552) and Air Force Office of Scientific Research (F49620-04-1-0032) is gratefully acknowledged.

Article outline:I. INTRODUCTIONII. BACKGROUNDA. Relationship to LESB. The Fourier transform of III. INERTIAL-RANGE MODEL OF A. A general form for in real spaceB. Scalar function in the inertial rangeC. Fitting to DNS dataIV. DISCUSSION AND IMPLICATIONS